GPS Heights Primer

•Chris Pearson1

•1National Geodetic Survey 2300 South Dirksen Pkwy Springfield IL

1) What types of heights are involved?• Orthometric heights• Ellipsoid heights• Geoid heights

2) How are these heights defined and related?

3) How accurately can these heights be determined?

To understand how to achieve GPS-derived orthometric heights at centimeter-level accuracy,

three questions must be answered:

Ellipsoid, Geoid, and Orthometric Heights

“Geoid”

Earth’s

Surface

Ocean

MeanSeaLevel

PO

PPlumb Line

Mass excess Mass deficiency

Ellipsoid

N

h

“h = H + NN”

H (Orthometric Height)N (Geoid Height)N (Geoid Height)h (Ellipsoid Height)

In Search of the Geoid…

Courtesy of Natural Resources Canada www.geod.nrcan.gc.ca/index_e/geodesy_e/geoid03_e.html

Leveled Height Differences

AC

B Topography

All Heights Based on Geopotential Number (CP)

The geopotential number is the potential energy difference between two points

g = local gravity WO = potential at datum (geoid) WP = potential at point

Why use Geopotential Number? - because if the GPN for two points are equal they are at the same potential and water will not flow between them

PP0

P

0

CWWdng

i

b

aia-b ghΔC

Heights Based on Geopotential Number (C)

• Normal Height (NGVD 29) H* = C / = Average normal gravity along plumb line

• Dynamic Height (IGLD 55, 85) Hdyn

= C / 45

45 = Normal gravity at 45° latitude

• Orthometric Height H = C / g g = Average gravity along the plumb line

• Helmert Height (NAVD 88) H = C / (g + 0.0424 H0) g = Surface gravity measurement (mgals)

GPS - Derived Ellipsoid Heights

Z Axis

X Axis

Y Axis

(X,Y,Z) = P (,,h)

h

Earth’sSurface

ZeroMeridian

Mean Equatorial Plane

Reference Ellipsoid

P

Ellipsoid Heights (NAD 83 vs. ITRF 00)

• NAD 83: Origin and ellipsoid (GRS-80) a = 6,378,137.000 meters (semi-major axis) 1/f = 298.25722210088 (flattening)

• ITRF 00: Origin (best estimate of earth’s C.O.M.)

• NAD 83 is non-geocentric relative to ITRF 00 origin by 1 - 2 meters

• ITRF 00 ellipsoid heights: Use a NAD 83 shaped ellipsoid centered at the ITRF 00 origin

• Ellipsoid height differences between NAD 83 and ITRF 00 reflect the non-geocentricity of NAD 83

Simplified Concept of ITRF 00 vs. NAD 83

2.2 meters

NAD 83Origin

ITRF 00Origin

Earth’s

Surface

h83

h00

Identically shaped ellipsoids (GRS-80)a = 6,378,137.000 meters (semi-major axis)1/f = 298.25722210088 (flattening)

North American Vertical Datum 1988(NAVD 88)

• Defined by one height (Father Point/Rimouski)

• Water-level transfers connect leveling across Great Lakes

• Adjustment performed in Geopotential Numbers

Vertical Control Network NAVD 88

NGVD 29 Versus NAVD 88NGVD 29 Versus NAVD 88Datum Considerations: NGVD 29 NAVD 88• Defining Height(s) 26 Local MSL 1 Local MSL •Tidal Epoch Various 1960-78

(18.6 years)Treatment of Leveling Data:• Gravity Correction Ortho Correction Geopotential Nos.

(normal gravity) (observed gravity)

• Other Corrections Level, Rod, Temp. Level, Rod, Astro, Temp, Magnetic, and Refraction Adjustments Considerations:

• Method Least-squares Least-squares

• Technique Condition Eq. Observation Eq.

• Units of Measure Meters Geopotential Units

• Observation Type Links Between Height Differences Junction Points Between Adjacent BMs

GPS-Derived Ellipsoid HeightGuidelines

• Basic concepts

• GPS Related Error Sources

• NOAA Technical Memorandum NOS NGS-58

San Francisco Bay Demonstration Project

CORS

GPS Site

BRIONE

CHABOT

WINTON

MOLATE

PT. BLUNT

L 1241

U 1320

S 1320

941 4290 N

941 4819 TIDAL 32

RV 223

941 4873 TIDAL 17

941 4863 TIDAL 5

R 1393

YACHT

N 1197

M 148

M 554

941 4750 TIDAL 7

PORT 1941 4779 ASFB 0 5 10

KM

Comparison of 30 Minute Solutions - Precise Orbit; Hopfield (0); IONOFREE(30 Minute solutions computed on the hour and the half hour)

MOLA to RV22 10.8 Km

Day 264dh (m)

Hours Diff.

Day 265dh (m)

Day 264 minus

Day 265 (cm)

* diff >2 cm

Mean dh (m)

Mean dh minus "Truth" (cm)

* diff >2 cm

14:00-14:30 -10.281 27hrs 17:00-17:30 -10.279 -0.2 -10.280 -0.514:30-15:00 -10.278 27hrs 17:30-18:00 -10.270 -0.8 -10.274 0.215:00-15:30 -10.281 27hrs 18:00-18:30 -10.278 -0.3 -10.280 -0.415:30-16:00 -10.291 27hrs 18:30-19:00 -10.274 -1.7 -10.283 -0.716:00-16:30 -10.274 27hrs 19:00-19:30 -10.274 0.0 -10.274 0.216:30-17:00 -10.287 27hrs 19:30-20:00 -10.276 -1.1 -10.282 -0.617:00-17:30 -10.279 27hrs 20:00-20:30 -10.261 -1.8 -10.270 0.617:30-18:00 -10.270 27hrs 20:30-21:00 -10.251 -1.9 -10.261 1.518:00-18:30 -10.277 21hrs 15:00-15:30 -10.270 -0.7 -10.274 0.218:30-19:00 -10.271 21hrs 15:30-16:00 -10.276 0.5 -10.274 0.219:00-19:30 -10.277 21hrs 16:00-16:30 -10.278 0.1 -10.278 -0.219:30-20:00 -10.271 21hrs 16:30-17:00 -10.286 1.5 -10.279 -0.320:00-20:30 -10.259 18hrs 14:00-14:30 -10.278 1.9 -10.269 0.720:30-21:00 -10.254 18hrs 14:30-15:00 -10.295 4.1 * -10.275 0.1

"Truth"14:00-21:00 -10.275 14:00-21:00 -10.276 0.1 -10.276

Two Days/Same Time

-10.254-10.251

> -10.253

Difference = 0.3 cm

“Truth” = -10.276Difference = 2.3 cm

Two Days/Different Times

-10.254-10.295

> -10.275

Difference = 4.1 cm

“Truth” = -10.276Difference = 0.1 cm

Precision With CORS

• How GPS positioning is affected by baseline length

• Varying length baselines formed from 19 CORS

• Dual Frequency Geodetic Receivers

• Post-Processed with a Precise Orbits

• Pairs of CORS sites forming 11 Baselines

• Baseline lengths ranging from 26 to 300 km

• Various Observation Session Durations (1, 2, 4, 6, 8, 12, and 24 hours)

0.000

0.010

0.020

0.030

rms

Up

(mete

rs)

25 50 75 100 125 150 175 200 225 250 275 300

Baseline Length (kilometers)

4 Hrs. 6 Hrs. 8 Hrs. 12 Hrs. 24 Hrs

Up rms Relative to DistanceMean rms - 10 Days of Observation

Recommendations to GuidelinesBased on These Tests

• Must repeat base lines Different days Different times of day

» Detect, remove, reduce effects due to multipath and having almost the same satellite geometry

• Must FIX integers

• Base lines must have low RMS values, i.e., < 1.5 cm

N O A A T e c h n ic a l M e m o r a n d u m N O S N G S - 5 8

G U ID E L I N E S F O R E S T A B L I S H I N G G P S - D E R I V E D E L L IP S O I D H E IG H T S( S T A N D A R D S : 2 C M A N D 5 C M )V E R S I O N 4 . 3

D a v id B . Z i lk o s k iJ o s e p h D . D 'O n o f r i oS t e p h e n J . F r a k e s

S i lv e r S p r i n g , M D

N o v e m b e r 1 9 9 7

U .S . D E P A R T M E N T O F N a t io n a l O c e a n ic a n d N a t io n a l O c e a n N a t io n a l G e o d e t icC O M M E R C E A t m o s p h e r ic A d m in is t r a t io n S e r v ic e S u r v e y

Available On-Line at

the NGS Web Site:

www.ngs.noaa.gov

Primary or SecondaryStation Selection Criteria

1. HPGN / HARN either FBN or CBN or CORS Level ties to A or B stability bench marks during this project

2. Bench marks of A or B stability quality Or HPGN / HARN previously tied to A or B stability BMs

• Special guidelines for areas of subsidence or uplift

Poured in place concrete post

Physically MonumentedPoints

Stainless steel rod driven to refusal

Disk in outcrop

Four Basic Control Requirements

• BCR-1: Occupy stations with known NAVD 88 orthometric heights Stations should be evenly distributed throughout project

• BCR-2: Project areas less than 20 km on a side, surround project with NAVD 88 bench marks i.e., minimum number of stations is four; one in each corner of project

• BCR-3: Project areas greater than 20 km on a side, keep distances between GPS-occupied NAVD 88 bench marks to less than 20 km

• BCR-4: Projects located in mountainous regions, occupy bench marks at base and summit of mountains, even if distance is less than 20 km

Equipment Requirements

• Dual-frequency, full-wavelength GPS receivers Required for all observations greater than 10 km Preferred type for ALL observations regardless of length

• Geodetic quality antennas with ground planes Choke ring antennas; highly recommended Successfully modeled L1/L2 offsets and phase patterns Use identical antenna types if possible Corrections must be utilized by processing software

when mixing antenna types

Data Collection Parameters

• VDOP < 6 for 90% or longer of 30 minute session Shorter session lengths stay < 6 always Schedule travel during periods of higher VDOP

• Session lengths > 30 minutes collect 15 second data Session lengths < 30 minutes collect 5 second data

• Track satellites down to 10° elevation angle

HARN or CORS Control Stations(75 km)

Primary Base(40 km)

Secondary Base(15 km)

Local Network Stations(7 to 10 km)

Appendix B. - - GPS Ellipsoid Height Hierarchy

Primary Base Stations

• Basic Requirements: 5 Hour Sessions / 3 Days

Spacing between PBS cannot exceed 40 km

Each PBS must be connected to at least its nearest PBS neighbor and nearest control station

PBS must be traceable back to 2 control stations along independent paths; i.e., base lines PB1 - CS1 and PB1 - PB2 plus PB2 - CS2, or PB1 - CS1 and PB1 - PB3 plus PB3 - CS3

Secondary Base Stations

• Basic Requirements: 30 Minute Sessions / 2 Days /Different times of day

Spacing between SBS (or between primary and SBS) cannot exceed 15 km

All base stations (primary and secondary) must be connected to at least its 2 nearest primary or secondary base station neighbors

SBS must be traceable back to 2 PBS along independent paths; i.e., base lines SB1 - PB1 and SB1 - SB3 plus SB3 - PB2, or SB1 - PB1 and SB1 - SB4 plus SB4 - PB3

SBS need not be established in surveys of small area extent

Local Network Stations

• Basic Requirements:

30 Minute Sessions / 2 Days / Different times of the day

Spacing between LNS (or between base stations and local network stations) cannot exceed 10 km

All LNS must be connected to at least its two nearest neighbors

LNS must be traceable back to 2 primary base stations along independent paths; i.e., base lines LN1 - PB1 and LN1 - LN2 plus LN2 - SB1 plus SB1 - SB3 plus SB3 - PB2, or LN1 - PB1 and LN1 - LN3 plus LN3 - SB2 plus SB2 - SB4 plus SB4 - PB3

Sample Project Showing Connections

CS1

PB2

SB2

LN4LN3LN2

LN5

LN1

SB1

SB3

SB5SB4 PB4

PB1

PB3

CS2

CS4CS3

38°16’NCORSHARNNAVD’88 BMNew StationSpacing Station

121°40’W122°20’W

37°55’N

LA

TIT

UD

E

LONGITUDE

Primary Base Station

8.2km

10LC

TIDD D191

MONT X469 Z190

DROU

BM20

04KU

TIDE

ZINCPT14

MART

5144

P371R100

LAKE

04HK

CATT

Q555

TOLA

East Bay Project Points

Primary Base StationsCORSHARNNAVD’88 BMNew Station

121°40’W122°35’W

37°50’N

38°20’N

LA

TIT

UD

E

LONGITUDE

Primary Base Station

MOLA

MARTLAKE

10CC

D191

29.6km25.8km

38.7k

m

19.0km

28.7km

25.7km 38.3km

31.6

km

CORSHARNNAVD’88 BMNew StationSpacing Station

121°40’W122°20’W

37°55’N

38°16’N

LA

TIT

UD

E

LONGITUDE

Primary Base Station

Session A

Session BSession C

Session D

Session ESession F

Session G

Observation Sessions

CORSHARNNAVD’88 BMNew StationSpacing Station

121°40’W122°20’W

37°55’N

38°16’N

LA

TIT

UD

E

LONGITUDE

Primary Base Station

8.2km

Independent Base Lines

A

A

A

AB

B

B

B

C

CC

C

D

D

DD

E

E

E

E

FF

F

F

G

G

GG

Observation Schedule

Basic Concept of Guidelines

• Stations in local 3-dimensional network connected to NSRS to at least 5 cm uncertainty

• Stations within a local 3-dimensional network connected to each other to at least 2 cm uncertainty

• Stations established following guidelines are published to centimeters by NGS

13,515 benchmarks remain in NGS database

28 % reported as “good” in last 10 years

NSRS benchmarks in Illinois

About 50 % are probably still usable

Benchmark availability

• There are 3881 Benchmarks in the NGSIDB for Alaska

• 663,268 sq mi

• Compared to 13,515 for Illinois

• 57,918 SQ. MI

CORSNetwork February

2010

~1445 Stations

So far added~50 (green dots)

CORS reprocessingon track. All data back to 1995 re-processed

CORSNetwork February

2010

Another 17 PBO sites will be added next week

Positioning America for the Future

NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION

National Ocean Service

National Geodetic Survey

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Horizontal Velocity MapHTDP Version 3.0

Test of Alaska secular field

Measurements Freymuller 2008

Source: Elliott, J. L., Freymueller J. T., and Rabus B. (2007), Coseismic deformation of the 2002 Denali fault earthquake: Contributions from synthetic aperture radar range offsets, J. Geophys. Res., 112, B06421, doi:10.1029/2006JB004428.

New Alaska data for HTDP, v 3.0includes dislocation model for the 2002 Denali earthquake

Multi-year CORS reprocessing Vertical

IGA Crustal deformation for the midwest

Crustal motion in Central Alaska

Alaska is subject to tectonic forcesCausing horizontal and vertical changes with timeThe vertical changes particularly are a challenge for height modernization activities in the state

Crustal motion data from Freymuller 2009Uplift data Larsen Pers .Com . 2009